Geodesic
One property of hereditary saturated formations
Problemy fiziki, matematiki i tehniki, no. 1 (2021), pp. 50-53

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Let $\mathfrak{F}$ be a hereditary saturated formation. It is proved that if for every Sylow subgroup $P$ of a finite group $G$ and every maximal subgroup $V$ of $P$ there is a $\mathfrak{F}$-subgroup $T$ such that $VT=G$, then $G\in\mathfrak{F}$. Problems 19.87 and 19.88 from the “Kourovka Notebook” are solved in the article.
Keywords: finite group, Sylow subgroup, supplement, generally subnormal subgroup, lattice formation.
Mots-clés : formation 
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X. Yi; S. F. Kamornikov; V. N. Tyutyanov. One property of hereditary saturated formations. Problemy fiziki, matematiki i tehniki, no. 1 (2021), pp. 50-53. http://geodesic.mathdoc.fr/item/PFMT_2021_1_a7/